3,786 research outputs found
Rate-invariant analysis of covariance trajectories
Statistical analysis of dynamic systems, such as videos and dynamic functional connectivity, is often translated into a problem of analyzing trajectories of relevant features, particularly covariance matrices. As an example, in video-based action recognition, a natural mathematical representation of activity videos is as parameterized trajectories on the set of symmetric, positive-definite matrices (SPDMs). The variable execution-rates of actions, implying arbitrary parameterizations of trajectories, complicates their analysis and classification. To handle this challenge, we represent covariance trajectories using transported square-root vector fields (TSRVFs), constructed by parallel translating scaled-velocity vectors of trajectories to their starting points. The space of such representations forms a vector bundle on the SPDM manifold. Using a natural Riemannian metric on this vector bundle, we approximate geodesic paths and geodesic distances between trajectories in the quotient space of this vector bundle. This metric is invariant to the action of the reparameterization group, and leads to a rate-invariant analysis of trajectories. In the process, we remove the parameterization variability and temporally register trajectories during analysis. We demonstrate this framework in multiple contexts, using both generative statistical models and discriminative data analysis. The latter is illustrated using several applications involving video-based action recognition and dynamic functional connectivity analysis
Log-Euclidean Bag of Words for Human Action Recognition
Representing videos by densely extracted local space-time features has
recently become a popular approach for analysing actions. In this paper, we
tackle the problem of categorising human actions by devising Bag of Words (BoW)
models based on covariance matrices of spatio-temporal features, with the
features formed from histograms of optical flow. Since covariance matrices form
a special type of Riemannian manifold, the space of Symmetric Positive Definite
(SPD) matrices, non-Euclidean geometry should be taken into account while
discriminating between covariance matrices. To this end, we propose to embed
SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW
approach to its Riemannian version. The proposed BoW approach takes into
account the manifold geometry of SPD matrices during the generation of the
codebook and histograms. Experiments on challenging human action datasets show
that the proposed method obtains notable improvements in discrimination
accuracy, in comparison to several state-of-the-art methods
Automatic Analysis of Facial Expressions Based on Deep Covariance Trajectories
In this paper, we propose a new approach for facial expression recognition
using deep covariance descriptors. The solution is based on the idea of
encoding local and global Deep Convolutional Neural Network (DCNN) features
extracted from still images, in compact local and global covariance
descriptors. The space geometry of the covariance matrices is that of Symmetric
Positive Definite (SPD) matrices. By conducting the classification of static
facial expressions using Support Vector Machine (SVM) with a valid Gaussian
kernel on the SPD manifold, we show that deep covariance descriptors are more
effective than the standard classification with fully connected layers and
softmax. Besides, we propose a completely new and original solution to model
the temporal dynamic of facial expressions as deep trajectories on the SPD
manifold. As an extension of the classification pipeline of covariance
descriptors, we apply SVM with valid positive definite kernels derived from
global alignment for deep covariance trajectories classification. By performing
extensive experiments on the Oulu-CASIA, CK+, and SFEW datasets, we show that
both the proposed static and dynamic approaches achieve state-of-the-art
performance for facial expression recognition outperforming many recent
approaches.Comment: A preliminary version of this work appeared in "Otberdout N, Kacem A,
Daoudi M, Ballihi L, Berretti S. Deep Covariance Descriptors for Facial
Expression Recognition, in British Machine Vision Conference 2018, BMVC 2018,
Northumbria University, Newcastle, UK, September 3-6, 2018. ; 2018 :159."
arXiv admin note: substantial text overlap with arXiv:1805.0386
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